High-Order Structure-Preserving Algorithms for Plasma Hybrid Models.

Wave-particle resonance plays a crucial role for the stability of burning plasma in magnetically confined fusion. We present provably stable algorithms for the accurate simulation of such (nonlinear) processes on long time scales. Our approach combines several recent advances in theoretical and numerical research: on the theoretical side, we rely on Hamiltonian fluid-kinetic hybrid models, largely based on the works of Tronci [37]. To achieve high-order discretization, we use finite element exterior calculus (FEEC) introduced by Arnold et al. [5] based on B-splines coupled with particle-in cell for the resonating particles. Last but not least, structure-preservation (in a sense to be defined more clearly in the text) is achieved by discretization of Poisson brackets, rather than PDEs - following the ideas of Kraus et al. [28]. These efforts culminate in the creation of the open-source software package STRUPHY (STRUcture-Preserving HYbrid codes) [1] which makes available to the scientific community a growing number of plasma hybrid codes, ready for use.